Critical Bands Theory and the Amplified, Stereo, and Recorded Sound

LMSC 207: Applied Acoustics Homework Assignment 6 Due Friday 30 April by 11:59pm EDT Please show your work for computational questions; I can and will award partial credit if some of your calculations are correct but your final answer is not, but if your answer is incorrect and you haven’t shown any work for it, I will have to award you 0 points for the question. Please write your answers on your own paper.
1. Find the critical bands of the following pairs of frequencies, and determine whether or not they “share” a critical band. (a) 100 Hz and 150 Hz (b) 1000 Hz and 1500 Hz (c) 6000 Hz and 6500 Hz a. 100 > 55-145 150 > 105- 195 = 105-145
yes they share a critical band
b.
1000 x 0.15 = 150 >> 1000-150= 850 1000+150= 1150 >> 850-1150HZ1500 x 0.15 – 225 >> 1500-225= 1225 1500+225 = 1725 >> 1225- 1725 HzNo they don’t share a critical band.
c. 6000 x 0.15 = 900 6000-900= 5100 6000+900 = 6900 .. 5100 – 6900 Hz
6500 x 0.15 =975 6500-975 = 5525 6500 +975 = 7475 5525-7475Hz
Critical band shared : 5525- 6900hz
2. Suppose a harmonic series has a fundamental of 800 Hz. Which harmonics will have a critical band to themselves, and at what point do the harmonics begin “sharing” critical bands? (To keep things simple, you can suppose the 15% rule applies to all frequencies in this harmonic series.)
3. Based on the theory of critical bands, explain why it is unwise to use dense chords in lower registers for melodic or harmonic reasons.
The theory of critical bands provides insight to how hearing works. Bands refer to a range of frequencies that are more detectable by the human hearing organ. Dense chords in lower registers are in the space that are not easy to hear in the human bandwidths of hearing. This is because some audio frequencies are harder in the perception of the first tone because of auditory masking.
4. (Round your answers to this question to the nearest 0.01 if needed.) Suppose an amplifier provides a power gain of 6.
P = IV
dB gain = 10 log(Power gain)P = IV = I 2R = V 2 R .
(a) What is the voltage gain provided by this amplifier?
Power gain = (Voltage gain)^2Power gain= 6
voltage gain = square root of 6
voltage gain = 2.44948974278= 2.45
(b) What is the decibel gain provided by this amplifier?
dB gain = 10 log(Power gain)
= 10 log (6)
=7.78151250384
= 7.78 dB
5. (Round your answers to this ques...